Optimal Control of Engine Warmup in Hybrid Vehicles

Reeven, van V Vital; Hofman, Théo; Willems, Frank; Huisman, Rgm Rudolf; Steinbuch, M Maarten

doi:10.2516/ogst/2014042

Cited by 7 publications

(5 citation statements)

References 21 publications

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“…Figure 7 shows that the optimal mode is changed at B 1 , B 2 and B 3 where the Hamiltonians of two modes are equal. Equating the Hamiltonians, using Equations (1), (4), (7), (36) and Table 6, results in five expressions, representing all the switching lines (guards B) where the optimal mode M * is changing. Two guards are a function of λ b ∀P d :…”

Section: Mode Selection Without Cost On Switchingmentioning

confidence: 99%

“…However, the system efficiency can be further improved by taking additional system states into account as suggested by [2,3], referred to as a 'unified', 'integrated', 'total' or 'holistic' energy management. Examples of such additional systems are the battery with its temperature and aging characteristics [4,5], engine after-treatment system [3,6], waste-heat recovery system [7], combustion engine [8], or the cabin heater [9].…”

Section: Introductionmentioning

confidence: 99%

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Multi-Level Energy Management for Hybrid Electric Vehicles—Part I

Reeven

Hofman

2019

Vehicles

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The fuel economy of a hybrid electric vehicle (HEV) is improved, by taking the energy relevant system states into account in the energy management system (EMS). With an increasing number of states and decision variables, energy optimizing algorithms in the EMS can be prohibitive for real-time implementation. In part I of this work, a model-based, multi-level approach is taken to subdivide the original (large) optimization problem into computational efficient sub-problems, based on optimal control techniques using a preview. The resulting EMS solves the problem of power-split between engine and motor/generator, mode and gear switching including switching costs, with battery energy constraints. The superior energy efficiency of the multi-level EMS is simulated on a representative heavy duty drive cycle, where it saves 7.0% fuel, compared to a conventional vehicle, where the baseline EMS for the HEV saves 5.8%. In part II, real-world validation of the EMS is performed.

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Section: Mode Selection Without Cost On Switchingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multi-Level Energy Management for Hybrid Electric Vehicles—Part I

Reeven

Hofman

2019

Vehicles

Self Cite

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“…Nevertheless we precise that several versions of the PMP were derived for (discrete) optimal control problems in which the dynamical system is described by a general difference equation (see, e.g., [8,37,41]). In these discrete versions of the PMP, the Hamiltonian maximization condition does not hold in general (see a counterexample in [8, Examples 10.1-10.4 p. [59][60][61][62]) and has to be replaced by a weaker condition known as the nonpositive Hamiltonian gradient condition (see e.g., [8,Theorem 42.1 p.330]).…”

Section: Introductionmentioning

confidence: 99%

“…Many examples can be found in mechanics and aerospace engineering (e.g., an engine may overheat or overload). We refer to [11,25,43,61,62] and references therein for other examples. State constrained optimal control problems are also important in management and economics (e.g., an inventory level may be limited in a production model).…”

Section: Introductionmentioning

confidence: 99%

Optimal sampled-data controls with running inequality state constraints: Pontryagin maximum principle and bouncing trajectory phenomenon

Bourdin

Dhar

2020

Math. Program.

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Sampled-data control systems have steadily been gaining interest for their applications in Engineering and Automation. In the present paper we derive a Pontryagin maximum principle for general nonlinear optimal sampled-data control problems in the presence of running inequality state constraints. In particular we obtain a nonpositive averaged Hamiltonian gradient condition associated to an adjoint vector being a function of bounded variations. As a well-known challenge, theoretical and numerical difficulties may arise in optimal permanent control problems with state constraints due to the possible pathological behavior of the adjoint vector (jumps and singular part lying on parts of the trajectory in contact with the boundary of the restricted state space). However, in our case of sampled-data controls, we find that, under certain general hypotheses, the optimal trajectory only contacts the running inequality state constraints at most at the sampling times. In that context the adjoint vector only experiences jumps at most at the sampling times (and thus in a finite number and at precise instants) and its singular part vanishes. Hence, taking advantage of this bouncing trajectory phenomenon, we are able to implement a numerical indirect method which we use to solve three simple examples.

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“…Once operating modes that are optimal under some assumptions according to PMP theory are obtained, the problem is reduced to finding the best combination of those modes to minimize fuel consumption on a cycle. Some works that use this philosophy are [36][37][38]. Also [39] shows similar concepts, but those operating modes are not deducted from PMP formulation but by observing PMP solutions to particular driving cycles.…”

Section: P Gmentioning

confidence: 99%

Analytical Optimal Solution to the Energy Management Problem in Series Hybrid Electric Vehicles

Luján

Guardiola

Plá

et al. 2018

IEEE Trans. Veh. Technol.

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Optimal solution to the energy management problem in hybrid electric vehicles has been extensively addressed in literature during last decade, especially with the application of dynamic programming, Pontryagin minimum principle or equivalent consumption minimization strategy. However, most of the works consist in finding cycle-specific optimal trajectories which are far from being general control strategies.The aim of this work is to derive an analytical expression, general and not cycle-specific, for the energy management problem that summarizes the optimal controls for a series hybrid electric vehicle. Starting from a simple definition of the powertrain, an explicit formulation is deducted to minimize fuel consumption based on an analytic analysis of Pontryagin minimum principle. Explicit expressions for control variables and costates are provided. The result is a general control strategy that specifies the optimal generator set usage for a given probability distribution of expected traction demands. This methodology is benchmarked with common methods in literature (dynamic programming and numerical Pontryagin minimum principle) showing near identical results but with strongly reduced computational time. The general form of this control strategy can also be used to analyze the optimal operation range of the engine, which could be useful for designing purposes.

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Optimal Control of Engine Warmup in Hybrid Vehicles

Cited by 7 publications

References 21 publications

Multi-Level Energy Management for Hybrid Electric Vehicles—Part I

Multi-Level Energy Management for Hybrid Electric Vehicles—Part I

Optimal sampled-data controls with running inequality state constraints: Pontryagin maximum principle and bouncing trajectory phenomenon

Analytical Optimal Solution to the Energy Management Problem in Series Hybrid Electric Vehicles

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